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The Mercator Sailing Problem

Below is a form using JavaScript that solves the Mercator Sailing problem:

Origin (Initial Position)

 
Latitude: degrees  minutes 
Longitude: degrees  minutes 

Destination (Final Position)

 
Latitude: degrees  minutes 
Longitude: degrees  minutes 
 

Results

Course to make : degrees true
Distance to make : nautical miles
Culmulative Distance : nautical miles

Sailing

Mercator SailingSailing is the term used in the maritime world to describe the method used to solve the problem of course and distance between two positions.

In broad terms, there are two main types of sailing, namely, the Rhumb Line sailing and the Great Circle sailing. The Mercator Sailing is the most accurate method employed in marine navigation to handle calculations related to Rhumb Line sailing.

Rhumb Line

It may be difficult to believe that if you sail on a constant course, except on exact East or exact West, you will end up at the North or the South pole, assuming there is no land in between. The constant course track that appears like a spiral on the Earth spheriod is called a Rhumb Line track.

Mercator Sailing

The plain triangle on the right indicates the plot of a Rhumb Line track on a Mercator chart between two points (A and C). By applying simple trigonometry principles the course and distance between the two positions can be determined.

The formulae for determining the values are :-

tan course = difference in Longitude / difference in Meridional Parts

Distance = difference in Latitude / cos course


Further Reading

Tools and more info

Misc



     
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